\((x-6)^2 - x(x+8) = 2\)

\(x^2 - 12x + 36 - x^2 - 8x = 2\)

\(-20x = 2 - 36\)

\(-20x = -34\)

\(x = \frac{-34}{-20} = \frac{17}{10} = 1.7\)
\(9x(x+6) - (3x+1)^2 = 1\)

\(9x^2 + 54x - (9x^2 + 6x + 1) = 1\)

\(9x^2 + 54x - 9x^2 - 6x - 1 = 1\)

\(48x = 2\)

\(x = \frac{2}{48} = \frac{1}{24}\)
\(y(y-1) - (y-5)^2 = 2\)

\(y^2 - y - (y^2 - 10y + 25) = 2\)

\(y^2 - y - y^2 + 10y - 25 = 2\)

\(9y = 27\)

\(y = 3\)
\(16y(2-y) + (4y-5)^2 = 0\)

\(32y - 16y^2 + 16y^2 - 40y + 25 = 0\)

\(-8y + 25 = 0\)

\(8y = 25\)

\(y = \frac{25}{8} = 3.125\)
\((x-5)^2 - x^2 = 3\)

\(x^2 - 10x + 25 - x^2 = 3\)

\(-10x = 3 - 25\)

\(-10x = -22\)

\(x = \frac{-22}{-10} = 2.2\)
\((2y+1)^2 - 4y^2 = 5\)

\(4y^2 + 4y + 1 - 4y^2 = 5\)

\(4y + 1 = 5\)

\(4y = 4\)

\(y = 1\)
\(9x^2 - 1 - (3x-2)^2 = 0\)

\(9x^2 - 1 - (9x^2 - 12x + 4) = 0\)

\(9x^2 - 1 - 9x^2 + 12x - 4 = 0\)

\(12x - 5 = 0\)

\(12x = 5\)

\(x = \frac{5}{12}\)
\(x + (5x+2)^2 = 25(1+x^2)\)

\(x + 25x^2 + 20x + 4 = 25 + 25x^2\)

\(26x + 4 = 25\)

\(26x = 21\)

\(x = \frac{21}{26}\)

Ответ: 1) 1.7; 2) 1/24; 3) 3; 4) 3.125; 5) 2.2; 6) 1; 7) 5/12; 8) 21/26.

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